A box contains one 2 inch rod, one 3 inch rod, one 4 inch rod, and one 5 inch rod. What is the maximum ...?

Question

number of different triangles that can be made using these rods as sides?

Answer 1

There are four rods in the box. Three are required to make a triangle, so there are only four possible combinations (leaving out each one of the four rods):

2-3-4 (leaving out 5) is a valid triangle
2-4-5 (leaving out 3) is a valid triangle
3-4-5 (leaving out 2) is a valid triangle

2-3-5 (leaving out 4) is not a triangle, since the longest side is equal to the sum of the other two sides. The longest side of a triangle must be less than the sum of the other two sides.